Solve for $x$ and $y$ using elimination. ${-x-3y = -10}$ ${-x-5y = -14}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-1$ ${-x-3y = -10}$ $x+5y = 14$ Add the top and bottom equations together. $2y = 4$ $\dfrac{2y}{{2}} = \dfrac{4}{{2}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {-x-3y = -10}\thinspace$ to find $x$ ${-x - 3}{(2)}{= -10}$ $-x-6 = -10$ $-x-6{+6} = -10{+6}$ $-x = -4$ $\dfrac{-x}{{-1}} = \dfrac{-4}{{-1}}$ ${x = 4}$ You can also plug ${y = 2}$ into $\thinspace {-x-5y = -14}\thinspace$ and get the same answer for $x$ : ${-x - 5}{(2)}{= -14}$ ${x = 4}$